Backward stochastic differential equations and applications to optimal control

Applied Mathematics & Optimization - Tập 27 - Trang 125-144 - 1993
Shige Peng1
1Department of Mathematics, Shandong University, Jinan, Shandong, People's Republic of China

Tóm tắt

We study the existence and uniqueness of the following kind of backward stochastic differential equation, $$x(t) + \int_t^T {f(x(s),y(s),s)ds + \int_t^T {y(s)dW(s) = X,} }$$ under local Lipschitz condition, where (Ω, ℱ,P, W(·), ℱt) is a standard Wiener process, for any given (x, y),f(x, y, ·) is an ℱt-adapted process, andX is ℱt-measurable. The problem is to look for an adapted pair (x(·),y(·)) that solves the above equation. A generalized matrix Riccati equation of that type is also investigated. A new form of stochastic maximum principle is obtained.

Tài liệu tham khảo

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